1. Field of the Invention
The present invention generally relates to an image forming apparatus and a belt unit.
2. Discussion of the Background
In general, an electrophotographic image forming apparatus, for example, a printer, a facsimile machine, a copier, a multifunction machine including at least two of these functions, etc., includes an image forming mechanism for forming an electrostatic latent image, developing the latent image with toner, and transferring the toner image onto a recording medium. The image forming apparatus further includes various movable belts including a photoreceptor belt, an intermediate transfer belt, a sheet transport belt, etc.
It is to be noted that “image forming” includes both forming on a recording medium an image including a pattern, etc., that has no commonly understood meaning as well as an image including a letter and/or an illustration that does have a given meaning. Thus, printing, imaging, recording, pattern forming, applying a material having a given function to a given position of a recording medium are synonymous with “image forming” in the descriptions below.
For example, a tandem image forming apparatus employing a direct transfer method includes a transport belt for transporting a recording medium and multiple image forming units for forming different color images (single color images) located along a direction in which the recording medium is transported. While the recording medium is transported through the image forming units, the different color images are superimposed one on another on the recording medium, forming a multicolor image thereon.
In another example, an inkjet image forming apparatus includes a recording head that applies different color ink droplets onto a recording medium in order to form a multicolor image thereon while a transport belt transports the recording medium.
In the image forming apparatuses described above, it is necessary to control travel of such movable belts accurately in order to prevent image failure such as color deviation, which means that the different color images are not properly aligned in the multicolor image.
In particular, travel velocity of the belts can fluctuate depending on various factors such as unevenness of belt thickness. For example, when a belt is produced through centrifugal burning using a cylindrical mold, its thickness may be uneven.
If the thickness of the belt is uneven, the belt moves faster when its thicker portion is on a driving roller and slower when its thinner portion is on the driving roller, thus causing its travel velocity to fluctuate. Fluctuation in travel velocity of the belt is described in detail below.
FIG. 16 illustrates an example of unevenness (or deviational distribution) in the circumferential direction of the thickness of the intermediate transfer belt (hereinafter simply “belt thickness”) used in the tandem image forming apparatus described above.
In FIG. 16, a horizontal axis shows a position on the intermediate transfer belt (belt position) in the circumferential direction when its circumferential length is shown as angle of 2π radian (rad). A vertical axis shows a deviation of the belt thickness in a circumferential direction from an average thickness of 100 μm, which is indicated as 0 in FIG. 16.
The deviational distribution of the belt thickness in a circumferential direction is also referred to as fluctuation in the belt thickness.
Here, “belt thickness unevenness” means deviational distribution of the belt thickness, as measured by a film thickness gauge, etc. The belt thickness can be uneven in either the circumferential direction in which the belt travels or a width direction, which is an axial direction of the roller and perpendicular to the direction in which the belt travels. By contrast, “belt thickness fluctuation” means another deviational distribution of the belt thickness that is caused by fluctuation in rotation cycle of the belt, and affects the travel velocity of the belt relative to a rotation velocity of the driving roller as well as a travel velocity of a driven roller relative to the travel velocity of the belt when the belt is mounted on a belt driving controller.
FIG. 17 illustrates a portion of a belt 1003 that is wound around a driving roller 1001, viewed from an axial direction of the driving roller 1001.
A travel velocity of the belt 1003 is determined based on a distance between a surface of the driving roller 1001 (hereinafter “roller surface”) and a belt pitch line, which is hereinafter referred to as a pitch line distance (PLD). The pitch line distance corresponds to a distance between a center of the belt in a thickness direction and its inner surface, in other words, the roller surface, provided that the belt 1003 is a uniform single-layer belt and absolute values of degrees of expansion of its inner surface and its outer surface are substantially similar.
Therefore, if the belt 1003 is single-layered, the relation between the pitch line distance and the belt thickness is substantially constant, and thus the travel velocity of the belt can be determined based on the belt thickness fluctuation.
By contrast, if the belt 1003 is multilayered, a harder layer and a softer layer can have different expansion characteristics, and thus its pitch line distance may differ.
The pitch line distance can be expressed as follows:PLD=PLDave+f(d)   (1)where PLDave represents an average value of the pitch line distance along the entire circumference of the belt 1003, which is hereinafter referred to as an average pitch line distance, and f(d) represents a function that indicates fluctuations in the pitch line distance in the entire circumference of the belt 1003.
In formula 1 described above, for example, the pitch line distance PLDave is 50 μm when the belt 1003 is single-layered and its average thickness is 100 μm. The function f(d) is a periodic function whose period corresponds to the circumference of the belt 1003, and is closely related to the deviation in the belt thickness shown in FIG. 16.
When the pitch line distance fluctuates in the circumferential direction, the travel velocity or travel distance of the belt 1003 relative to the rotational angular velocity or rotational displacement of the driving roller 1001 fluctuates, and, alternatively, the rotational angular velocity or rotational displacement of the driven roller 1001 relative to the travel velocity or travel distance of the belt 1003 fluctuates.
The relation between the travel velocity of the belt 1003 and the rotational angular velocity of the driving roller 1001 cab be expressed as:V={r+PLDave+kf(d)}ω  (2)where V represents the travel velocity of the belt 1003, r represents the radius of the driving roller 1001, ω represents the rotational angular velocity of the driving roller 1001, and k represents a PLD fluctuation effective coefficient.
It is to be noted that the PLD fluctuation effective coefficient k indicates a degree of effect of the pitch line distance fluctuation f(d) on the relations between the travel velocity of the belt 1003 and the rotational angular velocity of the driving roller 1001 or the travel distance of the belt 1003 and the rotational displacement of the driving roller 1001. This degree of effects of the fluctuation f(d) may vary depending on a state of contact between the belt 1003 and the driving roller 1001 or an amount for which the belt 1003 winds around the driving roller 1001.
Hereinafter r+PLDave+kf(d) is referred to as an effective roller radius, r+PLDave is referred to as an effective roller radius R, and f(d) is referred to as PLD fluctuation.
From formula 2 shown above, it can be seen that the relation between the travel velocity V of the belt 1003, which is hereinafter simply referred to as the belt travel velocity, and the rotational angular velocity ω of the driving roller 1001 varies depending on the PLD fluctuation f(d). That is, the belt travel velocity V varies depending on the PLD fluctuation f(d) even when the driving roller 1003 rotates at a constant rotational angular velocity (ω is constant).
When the belt 1003 is single-layered and a portion thicker than its average thickness winds around the driving roller 1001, the PLD fluctuation f(d), which is closely correlated with the belt thickness deviation, is a positive value, and thus the effective roller radius increases. Consequently, the belt travel velocity V increases even when the driving roller 1001 rotates at a constant rotational angular velocity.
By contrast, when a portion of the belt 1003 that is thinner than its average thickness winds around the driving roller 1001, the PLD fluctuation f(d) is a negative value, and thus the effective roller radius decreases. Consequently, the belt travel velocity V decreases even when the driving roller 1001 rotates at a constant rotational angular velocity.
Because the belt travel velocity V is not constant due to the PLD fluctuation f(d) even when the rotational angular velocity of the driving roller 1003 is constant as described above, the belt 1003 cannot be controlled to move at a desired travel velocity by adjusting only the rotational angular velocity ω of the driving roller 1001.
Further, relations between the belt travel velocity V and the rotational angular velocity of the driven roller is similar to the relations between the belt travel velocity V and the rotational angular velocity ω of the driving roller 1001. That is, formula 2 shown above can be used as well to calculate the belt travel velocity V based on a rotational angular velocity of the driven roller detected by a rotary encoder.
Therefore, when the belt 1003 is single-layered and a portion that is thicker than its average thickness winds around the driven roller, the PLD fluctuation f(d) is a positive value and thus the effective roller radius increases. Consequently, the rotational angular velocity of the driven roller decreases even when the belt travel velocity V is constant.
By contrast, when a portion of the single-layered belt 1003 that is thinner than its average thickness winds on the driven roller, the PLD fluctuation f(d) is a negative value, and thus the effective roller radius decreases. Consequently, the rotational angular velocity of the driven roller increases even when the belt travel velocity V is constant.
Thus, the travel velocity of the belt 1003 cannot be controlled by adjusting only the rotational angular velocity of the driven roller.
In order to solve the problem described above, there are the belt driving control methods or mechanisms described below, which take the PLD fluctuation f(d) into account.
A known method uses a belt produced through a centrifugal molding method, in which the PLD tends to fluctuate like a sine curve. Before the belt is installed in an apparatus, thickness profile (thickness unevenness) of the belt is measured along its entire circumference in the belt production process, and a velocity profile to cancel such fluctuation as to be caused by the thickness profile is preliminarily measured. Then, a reference position or home position that is used to match a phase of thickness profile data and that of the actual belt thickness unevenness is marked on the belt. Driving of belt is controlled in order to cancel the fluctuation in the belt travel velocity caused by the belt thickness fluctuation by detecting the marked position.
In another known method, a detection pattern is formed on the belt with toner, and periodic fluctuation in the belt travel velocity is detected by detecting the detection pattern with a sensor.
In another known method, a belt is looped around multiple support members including a driving rotary member and a driven rotary member, a rotational angular displacement or rotational angular velocity of the driven rotary member that does not contribute to transmission of rotational driving force is detected, and then an AC (alternating current) component of the rotational angular displacement or rotational angular velocity having a frequency corresponding to the periodic fluctuation in the belt thickness in a circumferential direction is extracted from results of the detection. Rotation of the driving rotary member is controlled based on the phase and amplitude of the AC component.
In a known driving control mechanism, a belt is looped around multiple support members including two rotary members of different diameters and/or that cause the PLDs of portions of the belt winding around thereof to differently affect the relations between the belt travel velocity and the rotational angular velocity thereof. Then, based on information about rotational angular displacement or rotational angular velocity of the two rotary members, rotation of the rotary members is controlled so as to reduce fluctuation in the belt travel velocity caused by the PLD fluctuation in the circumferential direction.
Yet another known driving control mechanism includes a mark detector configured to detect a reference position of a belt, an angular displacement deviation detector configured to detect deviation in angular displacement detected by an encoder, caused by fluctuation in belt thickness, according to an output signal from the mark detector, a first calculator configured to calculate a phase and a maximum amplitude of a distance between the mark and the deviation in the angular displacement, a nonvolatile memory storing results of the calculation generated by the first calculator, a second calculator configured to calculated correction data using values stored in the nonvolatile memory according to the distance from the mark on the belt, and a volatile memory storing the correction data. When the belt is driven, a belt driving member is controlled by adding the correction data to a control target value so as to cancel fluctuation in the belt travel velocity caused by fluctuation in belt thickness.
However, in the method using the belt thickness profile, a belt thickness measurement process is required, which increases the production cost. Further, each time the belt is replaced, the belt thickness profile data of the new belt must be input into the apparatus.
Further, in the method using the detection pattern, consumption of toner is relatively high because the detection pattern is formed on the entire circumference of the belt.
Moreover, in the method using the AC component of the rotational angular displacement or rotational angular velocity of the driven rotary member, although the belt thickness fluctuation is approximated by a sine function or a cosine function, approximating the belt thickness fluctuation to a periodic function is difficult.